# How do you write the quadratic in vertex form given y=-4x^2-5x+3?

May 5, 2015

$y = \left(- 4\right) {\left(x + \frac{5}{8}\right)}^{2} + \frac{73}{16}$

#### Explanation:

The general vertex form of a quadratic is
$y = m {\left(x - a\right)}^{2} + b$
where $\left(a , b\right)$ is the vertex

$y = - 4 {x}^{2} - 5 x + 3$

$y = \left(- 4\right) \left({x}^{2} + \frac{5}{4} x\right) + 3 \text{ extract the "m" factor}$

$y = \left(- 4\right) \left({x}^{2} + \frac{5}{4} x + {\left(\frac{5}{8}\right)}^{2}\right) - \left(- 4\right) {\left(\frac{5}{8}\right)}^{2} + 3$

$y = \left(- 4\right) {\left(x + \frac{5}{8}\right)}^{2} + \frac{73}{16}$

...and (assuming I haven't made any mistakes) the vertex is at $\left(- \frac{5}{8} , \frac{73}{16}\right) = \left(- \frac{5}{8} , 4 \frac{9}{16}\right)$